In this empirical study, the authors have assessed the accuracy of the VaR estimates obtained through the application of tail-index. The database consists of daily observations on two stock price indices in India, viz., BSE Sensex, and BSE100 for the period April 1, 1999 to March 31, 2005. The empirical results are quite encouraging. It is seen that returns on both of these index-portfolios do not follow a normal distribution. The non-normality is triggered primarily due to the excess-kurtosis problem, causing the underlying return distribution to have a fatter tail than normal. In order to handle the fat tail, the authors estimate the tail index, which measures the fatness of the tails. The estimated tail index is then used to estimate the Value-at-Risk (VaR). We observe that while normality assumption for return distribution in most cases leads to the underestimation of the VaR number, application of the Tail Index method improves the VaR estimates. The accuracy of these estimates is checked through the regulators' backtesting and Kupiec's tests. Results show that tail index based methods provide relatively more conservative VaR estimates and have a greater chance of passing through the regulators' backtesting. However, one should be careful while validating the VaR models, as the authors find that the performance of a VaR model may be sensitive to the sample size used in VaR estimation. Future research may extensively address this issue and check the robustness of the results across markets over a period of time.

In the hyper dynamic world of business, only changes in the risk level and its degree of impact are constant, and the risk managers have to live with and operate under risk. But managers can take the steps to minimize and hedge risk, and also to quantify the magnitude of the risk that still remains, so as to take precautionary measures to safeguard from the future unfavorable risky events. When we come to the issue of risk quantification, the traditional standard deviation method finds little relevance in the modern risk management practices. In contrast to variance, which measures the potential deviation of loss in either side of its expected level, risk managers are more interested to know precisely the amount of loss in monetary terms that they are likely to incur under certain circumstances. This led the growth and popularity of the concept of Value-at-Risk (VaR) equally among practitioners, researchers and academia. Among VaR methodologies, the “historical simulation” method is considered to be easy and arguably one of the most intuitive approaches. The main advantages of this method are that it provides full distribution of potential portfolio values and distributional assumptions need not be made. However, this method suffers from certain limitations, the major one being its inability to extrapolate and draw inferences about the distribution outside the sample-range/values.

To overcome the conceptual problems associated with historical simulation, an alternative method concentrates on fitting suitable parametric form for the probability distribution (either any standard distribution or hybrid distributions) of return and link the quantiles of the fitted distribution to the VaR. However, these methods are also not adequately reliable and may produce less accurate results for non-linear portfolios or for skewed/fat tailed distributions. The simplest parametric strategy is the covariance/normal method, which assumes normality of return distribution, either conditionally or unconditionally. But in reality, the financial market returns seldom follow normal distribution, which means that the simple covariance method may lead to produce unrealistic VaR numbers. But, there has been a vast body of literature dealing with non-normality. Based on existing studies, none of the methodologies is proved to be the
best in all situations/markets. So, practitioners face a problem of selecting the true distribution from the several alternatives. The task is difficult but has far-reaching consequences on profitability from an investment portfolio.

Applied Finance Journal, Indian Stock Market, Value-at-Risk, Risk Management, Investment Portfolio, Extreme Value Theory, National Stock Exchange, NSE, Financial Risks, Operational Risk, Ordinary Least-Square Technique, Market Risk.